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We propose related schemes to generate arbitrarily shaped single photons,i.e. photons with an arbitrary temporal profile, and coherent statesuperpositions using simple optical elements. The first system consists of twocoupled cavities, a memory cavity and a shutter cavity, containing a secondorder optical nonlinearity and electro-optic modulator (EOM) respectively.Photodetection events of the shutter cavity output herald preparation of asingle photon in the memory cavity, which may be stored by immediately changingthe optical length of the shutter cavity with the EOM after detection.On-demand readout of the photon, with arbitrary shaping, can be achievedthrough modulation of the EOM. The second scheme consists of a memory cavitywith two outputs which are interfered, phase shifted, and measured. States thatclosely approximate a coherent state superposition can be produced throughpostselection for sequences of detection events, with more photon detectionevents leading to a larger superposition. We furthermore demonstrate that`No-Knowledge Feedback' can be easily implemented in this system and used topreserve the superposition state, as well as provide an extra control mechanismfor state generation.

Measurement-based generation of shaped single photons and coherent state superpositions in optical cavities